Question

Three point charges +q, +2q and +Q are placed at the vertices of an equilateral triangle. If the potential energy of the system of three charges is zero, the value of Q in terms of q is

• A. \(-\frac{q}{3}\)
• B. \(\frac{-2q}{3}\)
• C. \(\frac{q}{2}\)
• D. \(\frac{3q}{2}\)

Hint:

For an infinite sheet the field is sigma over 2 epsilon, independent of distance.

Answer 1

The Correct Option is B

Step 1: Gauss's law with a pillbox:
A cylindrical surface through the sheet with area A on each end has flux $2EA$. The enclosed charge is $\sigma A$, so $2EA = \frac{\sigma A}{\varepsilon_0}$.

Step 2: Result:
$E = \frac{\sigma}{2\varepsilon_0}$, with no d in it. A graph of E against d is therefore a horizontal line, which is graph (C).

Final Answer:
Graph (C). \[ \boxed{\text{(C)}} \]